Surgeon General Integrity Restoration Act

Surgeon General Integrity Restoration Act - Amends the Public Health Service Act to establish a nomination procedure for selection of the Surgeon General. Requires the Institute of Medicine to submit to the Secretary of Health and Human Services and the President a list of ten qualified nominees. Requires the Secretary to recommend one nominee from such list, or provide an explanation as to why each nominee is unsatisfactory.

Requires the Surgeon General to submit an annual budget estimate.

Authorizes the Surgeon General to: (1) submit a draft of a speech or report to the Secretary or any employee of the Department of Health and Human Services (HHS) for comment and to issue, deliver, or release such speech or report notwithstanding any comment or objection of the Secretary or any such employee; and (2) directly hire staff without otherwise obtaining clearance or undergoing review as generally required within HHS.

Prohibits the censoring of any work product of the Surgeon General in any manner (except to comply with federal national security or privacy laws) by any federal entity or official for political reasons. Requires the Secretary to identify and separately label any supposed modifications to such a work product that the Surgeon General does not consent to accept.